How do you find the derivative of #f(x)=-4x^5+3x^2-5/x^2#?

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Answer 1 · 2017-04-09T19:37:39

#d/(d x) f(x)=(-20x^(16)+6x^5-10x)/x^4#

#f(x)=-4x^5+3x^2-5/x^2#

#d/(d x) f(x)=color(red)(d/(d x)( -4x^5))+color(blue)( d/(d x)(3x^2))-color(green)(d/(d x)(5/x^2))#

#color(red)(d/(d x)( -4x^5))=-20x^4#

#color(blue)(d/(d x)(3x^2))=6x#

#color(green)(d/(d x)(5/x^2))=(0*x^2-2x*5)/(x^2)^2=(-10x)/x^4#

#d/(d x) f(x)=-20x^4+6x-(10x)/x^4#

#d/(d x) f(x)=(-20x^(16)+6x^5-10x)/x^4#